Open AccessINWARD MOTIONS IN CONNECTED SPACES
Author(s) -
G. T. Whyburn
Publication year - 1969
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.63.2.271
Subject(s) - space (punctuation) , action (physics) , motion (physics) , function (biology) , mathematics , set (abstract data type) , pure mathematics , dendrite (mathematics) , fixed point , mathematical analysis , yield (engineering) , geometry , physics , computer science , classical mechanics , biology , quantum mechanics , evolutionary biology , programming language , operating system , thermodynamics
The concept of anA -set1 is broadened and developed in an arbitrary connectedT 1 -spaceX . Movements of such sets under arbitrary functions and under mildly restricted functions fromX to itself are analyzed. Areas of constricted action are located which are imposed on the function by the structure of the space. Applications are made to the case whereX is a dendrite. In this case existence of points of restricted motion is proved for arbitrary functions which yield actual fixed points in case of partly continuous functions.